Answers
Answer: It’s the second option
Step-by-step explanation:
Related Questions
Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) cos(x) sin(2x) sin(x) dx
Answers
Answer:
[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{4x-sin(4x)}{16} +c[/tex]
Step-by-step explanation:
Given
[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx[/tex]
Required
Evaluate
[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx[/tex]
Rewrite as:
[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \int\limits {cos(x)\ sin(x)\ sin(2x)} \, dx[/tex]
In trigonometry:
[tex]sin(2x) = 2\ sin(x)\ cos(x)[/tex]
Divide both sides by 2
[tex]\frac{1}{2}sin(2x) = \frac{2\ sin(x)\ cos(x) }{2}[/tex]
[tex]\frac{1}{2}sin(2x) = sin(x)\ cos(x)[/tex]
[tex]\frac{1}{2}sin(2x) = cos(x)\ sin(x)[/tex]
Substitute [tex]\frac{1}{2}sin(2x)[/tex] for [tex]cos(x)\ sin(x)[/tex]
[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \int\limits {\frac{1}{2}sin(2x)\ sin(2x)} \, dx[/tex]
[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \int\limits {\frac{1}{2}sin^2(2x)} \, dx[/tex]
[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{2}\int\limits {sin^2(2x)} \, dx[/tex]
Let [tex]u = 2x[/tex]
Differentiate:
[tex]du = 2 \ dx[/tex]
Make [tex]dx[/tex] the subject
[tex]dx = \frac{1}{2}du[/tex]
Substitute [tex]\frac{1}{2}du[/tex] for [tex]dx[/tex]
[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{2}\int\limits {sin^2(2x)} \, \frac{1}{2}du[/tex]
Substitute 2x for u
[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{2}\int\limits {sin^2(u)} \, \frac{1}{2}du[/tex]
[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{2}*\frac{1}{2}\int\limits {sin^2(u)} \, du[/tex]
[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{4}\int\limits {sin^2(u)} \, du[/tex]
At this point, we apply the reduction formula:
Which is:
[tex]\int\limits {sin^n(u)} \, du = \frac{n-1}{2}\int\limits sin^{n-2}(u)\ du\ - \frac{cos(u)sin^{n-1}(u)}{n}\du[/tex]
Let n = 2; So, we have:
[tex]\int\limits {sin^2(u)} \, du = \frac{2-1}{2}\int\limits sin^{2-2}(u)\ du\ - \frac{cos(u)sin^{2-1}(u)}{2}\du[/tex]
[tex]\int\limits {sin^2(u)} \, du = \frac{2-1}{2}\int\limits sin^{0}(u)\ du\ - \frac{cos(u)sin^{2-1}(u)}{2}\du[/tex]
[tex]\int\limits {sin^2(u)} \, du = \frac{1}{2}\int\limits sin^{0}(u)\ du\ - \frac{cos(u)sin^{2-1}(u)}{2}\du[/tex]
[tex]sin^0(u) = 1[/tex]
So, we have:
[tex]\int\limits {sin^2(u)} \, du = \frac{1}{2}\int\limits 1\ du\ - \frac{cos(u)sin^{2-1}(u)}{2}\du[/tex]
Integrate 1 with respect to u
[tex]\int\limits {sin^2(u)} \, du = \frac{1}{2}u - \frac{cos(u)sin^{2-1}(u)}{2}\du[/tex]
[tex]\int\limits {sin^2(u)} \, du = \frac{1}{2}u - \frac{cos(u)sin(u)}{2}\du[/tex]
Recall that:
[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{4}\int\limits {sin^2(u)} \, du[/tex]
So, we have:
[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{4}[ \frac{1}{2}u - \frac{cos(u)sin(u)}{2}\du][/tex]
Open bracket
[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{8}u - \frac{cos(u)sin(u)}{8}[/tex]
Recall that: [tex]u = 2x[/tex] and [tex]du = 2 \ dx[/tex] [tex]dx = \frac{1}{2}du[/tex]
So, the expression becomes:
[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{8}2x - \frac{cos(2x)sin(2x)}{8}[/tex]
[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{4}x - \frac{cos(2x)sin(2x)}{8}[/tex]
Add constant c
[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{4}x - \frac{cos(2x)sin(2x)}{8} +c[/tex]
----------------------------------------------------------------------------------------
In trigonometry:
[tex]sin(2\theta) = 2sin(\theta)cos(\theta)[/tex]
Divide both sides by 2
[tex]\frac{1}{2}sin(2\theta) = \frac{2sin(\theta)cos(\theta)}{2}[/tex]
[tex]\frac{1}{2}sin(2\theta) = sin(\theta)cos(\theta)[/tex]
Replace 2x with [tex]\theta[/tex]
[tex]\frac{1}{2}sin(2*2x) = sin(2x)cos(2x)[/tex]
[tex]\frac{1}{2}sin(4x) = sin(2x)cos(2x)[/tex]
----------------------------------------------------------------------------------------
[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{4}x - \frac{cos(2x)sin(2x)}{8} +c[/tex] becomes
[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{4}x - \frac{sin(4x)}{2*8} +c[/tex]
[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{4}x - \frac{sin(4x)}{16} +c[/tex]
[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{x}{4} - \frac{sin(4x)}{16} +c[/tex]
The solution can be further simplified as:
[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{4x-sin(4x)}{16} +c[/tex]
A loss of 10 pounds, can u help me please
Answers
Answer:
B
Step-by-step explanation:
A basketball player is 80 inches tall. A model of a basketball player is 5 inches tall. What is the scale factor?
Answers
Answer:
1/16
Step-by-step explanation:
divide 5 into 80 to get 16 which 5 is 1/16th of 80
What is the length of arc S shown below? Enter an exact expression. The angle in the figure is a central angle in radians.
Answers
Answer:
h
Step-by-step explanation:
n
Answer:
the answer is 18π/5
Step-by-step explanation:
A Central angle (θ) measured in radians tells us how many times the radius fits into the arc.
arc length ÷ radius = θ
arc length = θ · radius
S = 3π/5 · 6 cm
S = 18π/5 cm
Therefore the answer is 18π/5
A beverage distributor has a facility that bottles beer. Beer bottles are supposed to be filled to 12 oz but there are slight variations. As part of quality control, they randomly sample bottles of beer and measure how many ounces they contain. In the most recent sample, the found an average fill of 12.01 oz with a standard deviation of 0.89. Quantitative Question 2a If one of the bottles of sampled beer was filled to 10.98 oz, what is its associated zscore
Answers
Answer:
Its associated z-score is -1.16.
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In the most recent sample, the found an average fill of 12.01 oz with a standard deviation of 0.89.
This means that [tex]\mu = 12.01, \sigma = 0.89[/tex].
If one of the bottles of sampled beer was filled to 10.98 oz, what is its associated zscore
This is Z when X = 10.98. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{10.98 - 12.01}{0.89}[/tex]
[tex]Z = -1.16[/tex]
Its associated z-score is -1.16.
When three times a number is subtracted from 36, the result is 4 plus the number. What is the number?
Answers
Answer:
x = 8
The number is 8
Step-by-step explanation:
36 – (3x) = 4 + x
36 – (3 • 8) = 4 + 8
36 – 24 = 12
12 = 12
x = 8
I hope this helps.
The ferris wheel with a diameter of 150 feet at the fair is out of control and is moving at 60 degrees per second. How many miles per hour is someone moving as it spins out of control?
*There are 5,280 feet in a mile.
Answers
Answer:
Step-by-step explanation:
0.36x=-1.8
0.36x/0.36=-1.8/0.36
x=-5
What property was applied to solve this equation below?
Answers
Answer:
b, the division property of equality
Step-by-step explanation:
You are dividing both sides of the equation by 0.36 to solve
Find the volume of a triangular prisim with the following dimensions.
Base= 5
Height= 3
Length= 8
Answers
Answer:
60³
Step-by-step explanation:
Hi again.
This time we are working with a triangular prism which is a bit trickier than a rectangular prism but it is still pretty easy once you know the formula.
The formula for a triangular prism is :
V = 1/2 x b x h x l
Or in full terms :
Volume = 1/2 x Base x Height x Length
So basically we are going to plug in the base , height, and width like we did before but this time at the end we are going to divide it in half.
So like last time, lets look at what we are given :
Base = 5
Height = 3
Length = 8
And now we put these numbers into the formula :
Volume = 1/2 x Base x Height x Length
Volume = 1/2 x 5 x 3 x 8
Lets save the 1/2 for last and do the others first.
So we can do 5 x 3 and get 15.
Then 15 x 8 and we get 120.
Now the equation is literally :
Volume = 1/2 x 120
(This is the same as 120 / 2 just in multiplication terms)
So lets do this :
120 / 2
=
60
So now we have your answer :
Volume = 60³
(Don't forget the little 3)
Again, I hope this helps!
Any questions or concerns please comment or message me ofc :)
how do you solve this equation:
7-3 2/3
Answers
Answer:
5
Step-by-step explanation:
Using the order operations, we go left to right, multiplying 3 by 2/3, giving us 2. Then we subtract 7 - 2 = 5.
It is not possible to divide 5 by 0 because there is no number you can___ by 0 and get 5 .
Answers
Answer:
multiply
Step-by-step explanation:
Answer:
Yes, it's not possible to divide a number by 0.
Mentally solve 93 - 27 in as many ways as you can
Answers
Answer:
66
That is one way to solve it.
Answer:
93-27= 66
Step-by-step explanation:
B
6
8
A
х
D
с
x = [?]
Answers
9514 1404 393
Answer:
3
Step-by-step explanation:
The angle bisector BD makes left-side segments proportional to right-side segments. We see that CD is half of CB, so we expect the same proportion between AD and AB.
AD/AB = CD/CB
x/6 = 4/8 = 1/2 . . . . fill in the values, simplify the fraction
x = 6(1/2) . . . . . . . . multiply by 6
x = 3
People use water to cook, clean, and drink every day. An estimate of 17.3% of the water used each
day is for drinking. If a family uses 69.2 gallons of water a day for drinking, how many gallons do
they use every day?
Answers
Answer:
They use 4 gallons a day. Hope u helped!
Snack Packets
Number
Cost
($)
2
1.60
3
2.40
5
4.00
8
6.40
Answers
combine like terms to make a simple Hi, equivalent expression: 14-3+8x+7x
Answers
Answer:
11+15x
Step-by-step explanation:
combine 14 - 3 and 8x + 7x = 11 + 15x
3/4(8x -4) is equivalent to 3x - 2 + 3x - 1
true or flase
Answers
Answer:
true
Step-by-step explanation:
Hurry I am timed Which tiny, round “factory” puts together protein and is often found in the endoplasmic reticulum?
ribosome
chromosome
Golgi body
chloroplast
Answers
Answer:
the answer is ribsome
The ribosome serves as the site and carries the enzymes necessary for protein synthesis. They are often takes the shape of small round particles attached in the endoplasmic reticulum.
Evaluate the expression x + 8/27. Evaluate the expression for x=8/9
Answers
Answer: 32/27
Step-by-step explanation:
x = 8/9
x + 8 /27
[tex]\frac{8}{9} + \frac{8}{27} \\\\\frac{8}{9} * 3 = \frac{24}{27}\\\\\frac{24}{27} + \frac{8}{27}\\\\\frac{24 + 8}{27} \\\\\frac{32}{27}[/tex]
Answer:
Substitute the value of the variable into the equation and simplify.
Exact Form:
32 /27
Step-by-step explanation:
Find the equation of this line
Answers
Answer:
y = x+6
Step-by-step explanation:
You can see that (0,6) and (1,7) are points on the line, and the y-intercept of the line is 6.
Use the coordinates of these points to find the slope of the line.
slope = (7-6)/(1-0) = 1
y-intercept = 6
Slope-intercept equation for line of slope 1 that has y-intercept of 6:
y = x+6
what is the conjugate of 7+2√5
i don’t know how to do this please help
Answers
Decimal Form:
11.47213595
help me agaiaiiaiaiaiiaiain im too lazy to answer them
Answers
Answer: (C
Step-by-step explanation: To evaluate this, solve by raising 7 to the power of 3.
7 x 7 x 7
7 x 7 = 49 x 7 = 343
Therefore, the answer is C.
Pls help extra points and mark brainlist
Answers
Answer:
20 + 35x
Step-by-step explanation:
We have the expression 5(4 + 7x) and are asked to distrbute it.
When distributing, it's very simple, all you have to do is multiply the number outside the parenthesis with the numbers inside the parenthesis.
Therefore :
(5(4) + 5(7x))
20 + 35x
The ratio of red to blue marbles is 4 to 5. If there are 36 marbles
how many are blue?
Answers
Answer:
There are 45 blue marbles
Step-by-step explanation:
Well if 4 times 9 is 36, then 5 times 9 is 45
= 36 : 45
What is the measure of the obtuse angle in this figure?
Its not 180
Answers
Answer:
C
Step-by-step explanation:
7x+5=180
7x= 175
x- 25
so 5(25)+4= 129
which is C
if my answer helps please mark as brainliest.
Find the slope of the line through these two points: (-2, -1) and (10, 2).
[Write slope as a decimal, not a fraction.]
Answers
Answer:
[tex]y=0.25x-0.5[/tex]
Step-by-step explanation:
Firstly, the slope is [tex]\frac{3}{12} = 0.25[/tex], then you get the expression of the line.
Can someone please work out both problems, I need help with my math hw due in 4 hours
Answers
Answer:
I hope this helps
Step-by-step explanation:
This is not the same exact question but it shows you the throw down.
A+B+C= 180
so if A=60 and B=70
The sin is= 8
so 60+70= 130
130+c=180
130-180= 50
C=50
The following function is probability Distribution function.
F(x)=6x+1/25, x=0, 1, 2, 3, 4.
Determine the mean, μ, and variance, σ2, of the random variable. Round your answers to two decimal places.
Answers
Answer:
9.60 ; - 60.96
Step-by-step explanation:
Given the function :
F(x)=6(x+1) /25, x=0, 1, 2, 3, 4.
x = 0
F(0)=6(0+1)/25 = 6/25 = 0.24
x = 1
F(1)=6(1+1)/25 = 12/25 = 0.48
x = 2
F(2)=6(2+1)/25 = 18/25 = 0.72
x = 3
F(2)=6(3+1)/25 = 24/25 = 0.96
x = 4
F(2)=6(4+1)/25 = 30/25 = 1.2
X ______0 _____ 1 ______ 2 ______ 3 ____ 4
P(x) ___ 0.24 __ 0.48 ___ 0.72 ____ 0.96 __ 1.2
Mean, μ = Σx*p(x) :
(0*0.24) + (1*0.48) + (2*0.72) + (3*0.96) + (4*1.2)
= 9.60
Variance : Σx²*p(x) - μ²
(0^2*0.24) + (1^2*0.48) + (2^2*0.72) + (3^2*0.96) + (4^2*1.2) - 9.6^2
= 31.2 - 92.16
= - 60.96
Jack had 3 bottles of soda. Each bottle held 2 1/2 cups of soda. How many cups of soda did he have total?
Answers
Answer:
1 1/5 cups of soda.
Step-by-step explanation:
To solve this you need to change 3 and 2 1/2 into improper fractions so you get 6/2 and 5/2. Then you have to flip 5/2 so it becomes 2/5 and then you just have to cross cancel. Since the 2 from 2/5 can go into the 2 in 6/2 one time, 2/5 changes into 1/5 and 6/2 changes to 6/1. Now you can multiply across so 6 times 1 is 6 and 1 times 5 is 5 so you get 6/5. Now you have to change it into a mixed number which would be 1 1/5.
I hope this helps you :D
Clare has 80 pencils and 56 erasers to give away. What is the largest number of group that can formed with the same numbers of pencils and erasers in each group?
Answers
Answer:
56
Step-by-step explanation:
I assume each person in the group must have 1 pencil AND 1 eraser each.
Since you have more pencils than erasers, then the limiting factor is the number of erasers. So a group of 56 people will have 1 pencil And 1 eraser and Clare will have 24 pencils left over (assuming Clare has her own pencil and eraser - if not then the group size is 55 assuming Clare is not in the group)
sorry if it's too confusing
